Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 12.2, Problem 8P
Summary Introduction
Interpretation: Three Sigma Control Limits needs to be determined with the help of given data.
Concept Introduction: X bar chart monitors the change in mean over time and R chart monitors the change in range over time and helps organizations makes better improvement decisions.
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Checkout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed:
Sample
Mean
Range
Sample
Mean
Range
1
3.06
.42
4
3.13
.46
2
3.15
.50
5
3.06
.46
3
3.11
.41
6
3.09
.45
a. Using the factors in Table 10.3 , determine upper and lower limits for mean and range charts. b. Is the process in control?
Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons
produced each day, the mean and the range of this diameter have been as follows:
a) What is the value of x?
x= 156.76 mm (round your response to two decimal places).
b) What is the value of R?
Day
1
2
3
4
5
Mean x
(mm)
158.9
155.2
155.6
157.5
156.6
R = 4.40 mm (round your response to two decimal places).
c) What are the UCL and LCL using 3-sigma?
Upper Control Limit (UCL) = mm (round your response to two decimal places).
Range R
(mm)
4.2
4.4
4.3
4.8
4.3
Ç
8. Control charts for X and R are maintained on the shear strength of spot welds. One
hundred observations divided into subgroups of size five are used as a baseline to
construct the charts, and estimates of u and o are computed from these observa-
tions. Assume that the 100 observations are X1, X2, . . . , X100 and the ranges of the
20 subgroups are R1, R2, . . . , R20. From these baseline data the following quanti-
ties are computed:
100
20
ΣΧ- 97,500, ΣR- 1,042.
Using this information, compute the values of three-sigma limits for both charts.
Chapter 12 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 12.1 - Prob. 2PCh. 12.1 - Prob. 3PCh. 12.1 - Prob. 4PCh. 12.1 - Prob. 5PCh. 12.1 - Prob. 6PCh. 12.2 - Prob. 7PCh. 12.2 - Prob. 8PCh. 12.2 - Prob. 9PCh. 12.2 - Prob. 10PCh. 12.2 - Prob. 11P
Ch. 12.2 - Prob. 12PCh. 12.2 - Prob. 13PCh. 12.3 - Prob. 14PCh. 12.3 - Prob. 15PCh. 12.3 - Prob. 16PCh. 12.3 - Prob. 17PCh. 12.4 - Prob. 18PCh. 12.4 - Prob. 19PCh. 12.4 - Prob. 20PCh. 12.4 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Prob. 24PCh. 12.6 - Prob. 25PCh. 12.6 - Prob. 26PCh. 12.6 - Prob. 27PCh. 12.6 - Prob. 28PCh. 12.9 - Prob. 29PCh. 12.9 - Prob. 30PCh. 12.9 - Prob. 31PCh. 12.9 - Prob. 32PCh. 12.9 - Prob. 33PCh. 12.10 - Prob. 34PCh. 12.10 - Prob. 35PCh. 12.10 - Prob. 37PCh. 12.10 - Prob. 38PCh. 12.10 - Prob. 39PCh. 12.10 - Prob. 40PCh. 12.11 - Prob. 41PCh. 12.11 - Prob. 42PCh. 12.11 - Prob. 43PCh. 12.11 - Prob. 44PCh. 12.12 - Prob. 46PCh. 12.12 - Prob. 47PCh. 12.12 - Prob. 48PCh. 12 - Prob. 49APCh. 12 - Prob. 50APCh. 12 - Prob. 51APCh. 12 - Prob. 52APCh. 12 - Prob. 53APCh. 12 - Prob. 54APCh. 12 - Prob. 55APCh. 12 - Prob. 57APCh. 12 - Prob. 58APCh. 12 - Prob. 59APCh. 12 - Prob. 60APCh. 12 - Prob. 61APCh. 12 - Prob. 62APCh. 12 - Prob. 63APCh. 12 - Prob. 64APCh. 12 - Prob. 65APCh. 12 - Prob. 66APCh. 12 - Prob. 67APCh. 12 - Prob. 68APCh. 12 - Prob. 69APCh. 12 - Prob. 70AP
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